Three-dimensional measurement techniques are widely used in product testing and process control, medical treatment, protection of historical relics, aviation and aerospace, and cultural domains, because they can describe three-dimensional characteristics of objects and obtain three dimensional information of object surfaces.
The optical grating projection method is an important three-dimensional measuring technique which includes height information of an object in the gratings in the form of phase by projecting sinusoidal grating onto the surface of the object, utilizes CCD to obtain the grating fringe pattern of the object surface, and employs a specific algorithm to process the fringe pattern to extract the phase, so as to establish three dimensional information of the object. Commonly-used methods for solving the phase of a fringe pattern include phase-shift method, Fourier transform method, windowed Fourier transform method, and wavelet transform method, etc.
The Fourier transform method is widely used, since it can accomplish phase measurement by acquiring only one fringe pattern and thus can achieve dynamic measurement. However, Fourier transform is a global signal analysis tool. It can't extract local signal characteristics and has spectrum aliasing problems during transformation, which may influence the accuracy of phase measurement. In recent years, with rapid development of the wavelet analysis theory, wavelet transform was introduced into the domain of three-dimensional optical measurement. A technique has been developed to analyze fringe patterns by means of wavelet transform and thereby achieve three-dimensional measurement of objects, and the technique is referred to as wavelet transform profilometry. Wavelet analysis is an effective tool for analyzing non-stable signals. Compared to the conventional Fourier transform that has been widely used in the signal processing domain, wavelet transform has an advantage in the analysis of local signal characteristics. Due to the characteristic of multi-resolution analysis, a wavelet transform can not only obtain global signal characteristics like a Fourier transform, but also analyze details of local signals, and therefore has better time/spatial locality. Therefore, solving the phase of a fringe pattern by means of wavelet transform can avoid the spectrum-aliasing problem emerged in Fourier transform and achieve higher measurement accuracy.
As the phase value solved by means of wavelet transform is always within the range of 0-2π, a phase unwrapping procedure is required. To achieve dynamic measurement, usually no secondary pattern is added to increase information and help phase unwrapping. Though the simple scan-line phase-unwrapping method has a high speed of calculation, it doesn't have enough robustness and is prone to error propagation. The quality map guided phase-unwrapping algorithm chooses a best-phase unwrapping path by creating a quality map that reflects the reliability of each pixel point of the fringe pattern. This method has higher robustness and can accomplish phase unwrapping more accurately, but it has a longer operation time and therefore is not suitable for real-time measurement.
A key procedure for the quality map guided phase unwrapping algorithm is the creation of a quality map. A quality map can be created mainly with the following methods. Phase gradient method: the maximum phase gradient between a point and its neighboring points is taken as the quality value of the point. The higher the quality value, the poorer the quality of the point. Surface vector quality map method: the inner product of a normal vector at each point and a negative unit vector in the CCD projection direction is taken as the quality value of the point, wherein, the normal vector can be calculated from the phase values of the point and its neighboring points. Neither of the above two methods involves wavelet transform parameters, and therefore are not applicable to wavelet transform profilometry. Wavelet transform ridge amplitude method: a quality map is created with the modulus at a wavelet transform ridge to guide initial phase unwrapping, under the principle that the modulus at the wavelet transform ridge represents the similarity degree between local signal and wavelet function. This method takes full advantage of the matrix obtained from wavelet transform, but such a quality map creation method doesn't take account of the scale factor at the wavelet transform ridge, which is to say, when the scale factor at the wavelet transform ridge becomes too high or too low, the modulus can't accurately reflect the quality of the local signal; in addition, as the amplitude of a local signal varies, the amplitude at the wavelet ridge in the wavelet transform matrix will vary, therefore the amplitude can't be accurately described with regard to the sinusoidal characteristic and reliability of the local signal.